To determine which triangles are congruent using the SSS (Side-Side-Side) Congruence Theorem, we will compare the side lengths of each triangle.
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Triangle #1 (sides: 2.5 cm, 6.75 cm, 8 cm)
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Triangle #2 (angle: 60° between sides: 2.5 cm and 8 cm)
- To apply the SSS theorem, we need to find the length of the third side of Triangle #2 using the Law of Cosines:
Here, , , and .
- To apply the SSS theorem, we need to find the length of the third side of Triangle #2 using the Law of Cosines:
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Triangle #3 (angle: 111.17° between sides: 2.5 cm and 6.75 cm, third side: 8 cm)
- We already have one side
, and the two other sides cm and cm.
- We already have one side
Now we compare the side lengths:
- For Triangle #1: 2.5 cm, 6.75 cm, and 8 cm.
- For Triangle #3: The sides are 2.5 cm, 6.75 cm, and 8 cm.
Since Triangle #3 has the same three side lengths as Triangle #1, they are congruent by SSS.
Conclusion:
Triangle #1 and Triangle #3 are congruent.
So, the answer is: Triangle #1 and Triangle #3 are congruent.